TY - JOUR
T1 - Some observations about dissipative properties for dynamical systems under change of variables
AU - Fernández-Anaya, Guillermo
AU - Flores-Godoy, José Job
PY - 2011
Y1 - 2011
N2 - This note gives results about the preservation of some dissipative properties of systems under a change of variables. In the textbooks it is not mentioned explicitly the relationship between the equations associated with the dynamics of a system and the selected Lyapunov function to establish its stability property, when a change of coordinates is used. Based on the fact that Lyapunov stability is preserved under these changes of variables, it is shown that various forms of dissipativity can be preserved. In addition, we will show that the input-state stability (ISS), integral input-to-state stability (iISS) and input/output to state stability (IOSS) can be preserved under this class of transformation. Some examples are given to show these results.
AB - This note gives results about the preservation of some dissipative properties of systems under a change of variables. In the textbooks it is not mentioned explicitly the relationship between the equations associated with the dynamics of a system and the selected Lyapunov function to establish its stability property, when a change of coordinates is used. Based on the fact that Lyapunov stability is preserved under these changes of variables, it is shown that various forms of dissipativity can be preserved. In addition, we will show that the input-state stability (ISS), integral input-to-state stability (iISS) and input/output to state stability (IOSS) can be preserved under this class of transformation. Some examples are given to show these results.
KW - Change of coordinates
KW - Preservation of dissipativity
KW - Preservation of input-state stability
KW - Preservation of input/output to state stability
KW - Preservation of integral input-to-state stability
UR - http://www.scopus.com/inward/record.url?scp=84858784411&partnerID=8YFLogxK
U2 - 10.2174/1874110X01105010053
DO - 10.2174/1874110X01105010053
M3 - Artículo
AN - SCOPUS:84858784411
SN - 1874-110X
VL - 5
SP - 53
EP - 60
JO - Open Cybernetics and Systemics Journal
JF - Open Cybernetics and Systemics Journal
IS - 1
ER -